Question: Simplify the following expression: $p = \dfrac{8x^2 - 64x - 72}{x - 9} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $8$ , so we can rewrite the expression: $ p =\dfrac{8(x^2 - 8x - 9)}{x - 9} $ Then we factor the remaining polynomial: $x^2 {-8}x {-9} $ ${-9} + {1} = {-8}$ ${-9} \times {1} = {-9}$ $ (x {-9}) (x + {1}) $ This gives us a factored expression: $\dfrac{8(x {-9}) (x + {1})}{x - 9}$ We can divide the numerator and denominator by $(x + 9)$ on condition that $x \neq 9$ Therefore $p = 8(x + 1); x \neq 9$